Can you please check if the proclog folder has file starting with "ag_ping*" or log files generated at the time of fluctuation. please check those log files for any specific error statement & post it here.

Those are not the default values, I suspect the person who originally installed the Agent had their reasons for using them instead of the defaults (i.e. 7005/7006).

The ports are not officially reserved for Control-M but are usually recognised as "standard" to be used for the Control-M Agent. However I have found other products that sometimes use the same (e.g. Peoplesoft) and obviously you cannot guarantee a lost & confused admin (who doesn't know that Control-M was there first) might mistakenly use them.